poj 1543 & HDU 1334 & ZOJ 1331 Perfect Cubes(数学 暴力大法好)

题目链接：http://poj.org/problem?id=1543

Description

For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation a^3 = b^3 + c^3 + d^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {a,b,c,d} which satisfy this equation for a <= N.

Input

One integer N (N <= 100).

Output

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

Sample Input

24

Sample Output

Cube = 6, Triple = (3,4,5)
Cube = 12, Triple = (6,8,10)
Cube = 18, Triple = (2,12,16)
Cube = 18, Triple = (9,12,15)
Cube = 19, Triple = (3,10,18)
Cube = 20, Triple = (7,14,17)
Cube = 24, Triple = (12,16,20)

Source

Mid-Central USA 1995

题目链接：

寻找：a^3 = b^3 + c^3 + d^3 。

代码如下：（POJ）

#include <cstdio>
#include <cstring>
int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        for(int i = 3; i <= n; i++)
        {
            for(int j = 2; j < n; j++)
            {
                for(int k = j+1; k < n; k++)
                {
                    for(int l = k+1; l < n; l++)
                    {
                        if(i*i*i==j*j*j+k*k*k+l*l*l)
                            printf("Cube = %d, Triple = (%d,%d,%d)\n",i,j,k,l);
                    }
                }
            }
        }
    }
    return 0;
}

（HDU & ZOJ）

#include <cstdio>
#include <cstring>
int main()
{
    for(int i = 3; i <= 200; i++)
    {
        for(int j = 2; j < 200; j++)
        {
            for(int k = j+1; k < 200; k++)
            {
                for(int l = k+1; l < 200; l++)
                {
                    if(i*i*i==j*j*j+k*k*k+l*l*l)
                        printf("Cube = %d, Triple = (%d,%d,%d)\n",i,j,k,l);
                }
            }
        }
    }
}